Dephasing of Kuramoto oscillators in kinetic regime towards a fixed asymptotically free state
We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular free state, if the interaction is small enough, it exists a solution which converges to it. For this class of solution the order parameter vanishes to zero, showing a behavior similar to the phenomenon of Land...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sapienza Università Editrice
2014-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2014(3-4)/189-206.pdf |
| Summary: | We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular free state, if the interaction is small enough, it exists a solution which converges to it. For this class of solution the order parameter vanishes to zero, showing a behavior similar to the phenomenon of Landau damping in plasma physics. We obtain an exponential decay of the order parameter in the case on analytical regularity of the asymptotic state, and a polynomial decay in the case of Sobolev regularity. |
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| ISSN: | 1120-7183 2532-3350 |